axis- the straight line around which an object may rotate or revolve.
rotation (spin)- a spinning motion that takes place when an object rotates about an axis; located within the object.
revolution- motion of an object turning around an axis; located outside the object.
The difference of rotation and revolution and shown here.
Ch.9 Section 2-Rotational Speed
linear speed- the path distance moved per unit of time; also called speed.
With linear speed, a point on the outer edge of an object moves a greater distance in one rotation than a point closer to the center of the object.
This means that the point on the outer edge has a greater linear speed than the point closer to the axis.
As you can see, as the person moves toward the outer edge of a rotating platform, her linear speed, represented by the blue arrows, must increase if she is to maintain her position relative to the ground.
tagential speed- the speed of an object moving along a circular path.
This term is used because the direction of the object's motion is always tangent to the circle.
When dealing with circular motion, both linear speed and tangential speed can be used to describe the object in motion.
Tangential speed depends on the rotational speed and distance from the axis.
At the axis of an object, there is no tangential speed
The tangential speed, shown with the red arrows, is the path of the objects motion if it were to separate from it's rotation around the circle.
rotational speed (angular speed)- the number of rotations or revolutions per unit of time; often measured in rotations or revolutions per second or per minute (RPM).
All parts of a rotating object rotate around the axis in the same amount of time.
This means, that anywhere on the object, the rate of rotation is the same.
Tangential speed is directly proportional to the rotational speed and the radius distance from the axis of the object.
Tangential speed ~ radial distance x rotational speed
At the center of an object, there is rotational speed. As you move further from the axis, the tangential speed increases while the rotational speed remains the same.
As shown in this diagram, the two speeds, tangential and rotational, are represented in one equation: tangential speed= radial distance * angular speed
or v = (r)(w) Ch.9 Section 3-Centripetal Force
centripetal force- a center directed force that causes an object to move in a curved (sometimes circular) path.
Centripetal means "center-seeking" or "toward the center".
It is any force that is at a right angle to the path of a moving object that has a circular motion.
As you can see by this picture, when on a roller coaster that has a loop, the passengers experience centripetal force, as well as inertia.
Centripetal force can be found with the following equation: Fc = ((mv)^2) / (r) = ((m)(r)(w))^2 where
Fc= Centripetal Force ;m= mass; r= radius; v= tangential speed; w= angular speed
Ch.9 Section 4-Centripetal and Centrifugal Forces
centrifugal force- an apparent outward force on a rotating or revolving body. It is fictitious in the sense that it is not part of an interaction, but is due to the tendency of a moving body to move in a straight line path.
Centrifugal force means "center-fleeing" or "away from the center".
One may believe that centrifugal force pulls something outward, while reality is that there is only an absence of centripetal force.
The "centripetal-force effect" is only attributed to inertia (which is the tendency of a moving body to follow a continuous straight line path)
As seen in this picture, the people on the ride experience an outward force as the swings move in a circular pattern.
Ch.9 Section 5-Centrifugal Force in a Rotating Reference
In a rotating reference, a centrifugal force feels as though it acts like gravity.
However, both centripetal force (towards the center of the axis), and the centrifugal force (pulling outward) are acting upon the object in the rotating reference.
Gravity can only occur between two masses (our mass and the earth for example).
In a rotating object with a centrifugal force, there is no second mass for the object to be attracted to. This means that a centrifugal force is only an effect of rotation (not a true force).
It is because of this "false force" that physicists refer to centrifugal force as a fictitious force.
It is important to remember that centrifugal force is always present in a rotating reference.
This image shows the centrifugal force moving outward during a rotation. Ch.9 Section 6-Simulated Gravity
Gravity is simulated by centrifugal force
For example:
If someone were inside a wheel the direction "up" is toward the center of the wheel and "down" is radically outward.
Doubling the distance from the axis of rotation doubles the centripetal/centrifugal acceleration; tripling the distance, triples the acceleration, and so on.
At the axis, the radical distance is zero and there is no acceleration due to rotation.
Small-diameter structures would have to rotate at high speeds to provide a simulated gravitational acceleration of 1g.
Simulated gravity can be represented by a space station. Practice Problems The following practice problems were assigned by Mr. Strong and are found in the textbook:
Sections:
Ch.9 Section 1-Rotation and Revolution
The difference of rotation and revolution and shown here.
Ch.9 Section 2-Rotational Speed
As you can see, as the person moves toward the outer edge of a rotating platform, her linear speed, represented by the blue arrows, must increase if she is to maintain her position relative to the ground.
The tangential speed, shown with the red arrows, is the path of the objects motion if it were to separate from it's rotation around the circle.
As shown in this diagram, the two speeds, tangential and rotational, are represented in one equation:
tangential speed= radial distance * angular speed
or
v = (r)(w)
Ch.9 Section 3-Centripetal Force
As you can see by this picture, when on a roller coaster that has a loop, the passengers experience centripetal force, as well as inertia.
Centripetal force can be found with the following equation:
Fc = ((mv)^2) / (r) = ((m)(r)(w))^2
where
Fc= Centripetal Force ;m= mass; r= radius; v= tangential speed; w= angular speed
Ch.9 Section 4-Centripetal and Centrifugal Forces
As seen in this picture, the people on the ride experience an outward force as the swings move in a circular pattern.
Ch.9 Section 5-Centrifugal Force in a Rotating Reference
This image shows the centrifugal force moving outward during a rotation.
Ch.9 Section 6-Simulated Gravity
Simulated gravity can be represented by a space station.
Practice Problems
The following practice problems were assigned by Mr. Strong and are found in the textbook:
Pages 133-134 Review Questions # 3, 4, 7, 8, 10, 12, 13, 15, 16, 17
Pages 134-135 Think and Explain # 1, 2, 3, 4, 7, 8, 9, 10, 11
Page 135 Think and Solve # 1, 2, 3, 4
Sources